tough binomial function question!! help!!

Watch
bored_user:)
Badges: 22
Rep:
?
#1
Report Thread starter 1 month ago
#1
There's the question.
0
reply
bored_user:)
Badges: 22
Rep:
?
#2
Report Thread starter 1 month ago
#2
Name:  image-42d87e92-0d62-4a82-810c-79623961883c1919796440032539541-compressed.jpg.jpeg
Views: 8
Size:  94.6 KB
part 2 pls
0
reply
mqb2766
Badges: 18
Rep:
?
#3
Report 1 month ago
#3
(Original post by bored_user:))
Name:  image-42d87e92-0d62-4a82-810c-79623961883c1919796440032539541-compressed.jpg.jpeg
Views: 8
Size:  94.6 KB
part 2 pls
The binomial coeffs are an expansion of
(1+x)^n
When x=1
Last edited by mqb2766; 1 month ago
0
reply
bored_user:)
Badges: 22
Rep:
?
#4
Report Thread starter 1 month ago
#4
(Original post by mqb2766)
The binomial covers are an expansion of
(1+x)^n
When x=1
So do I write (1+x)^n = 2^n

and then sent x=1?
0
reply
RDKGames
Badges: 20
Rep:
?
#5
Report 1 month ago
#5
(Original post by bored_user:))
So do I write (1+x)^n = 2^n

and then sent x=1?
No.

Firstly, can you represent (1+x)^n as a sum of increasing powers of x using the binomial theorem?

Then substitute x=1 into both sides of this relation.

Result falls out.
0
reply
mqb2766
Badges: 18
Rep:
?
#6
Report 1 month ago
#6
Expand (1+x)^n
Then set x=1 in both the expansion and the original expression.
0
reply
bored_user:)
Badges: 22
Rep:
?
#7
Report Thread starter 1 month ago
#7
(Original post by RDKGames)
No.

Firstly, can you represent (1+x)^n as a sum of increasing powers of x using the binomial theorem?

Then substitute x=1 into both sides of this relation.

Result falls out.
So is this the answer?

Name:  image-98e06cfd-5ee0-447d-9294-3943746bdea33349879676836789606-compressed.jpg.jpeg
Views: 7
Size:  21.3 KB
0
reply
bored_user:)
Badges: 22
Rep:
?
#8
Report Thread starter 1 month ago
#8
(Original post by mqb2766)
Expand (1+x)^n
Then set x=1 in both the expansion and the original expression.
How do I even expand that when n has no value??
0
reply
mqb2766
Badges: 18
Rep:
?
#9
Report 1 month ago
#9
(Original post by bored_user:))
So is this the answer?

Name:  image-98e06cfd-5ee0-447d-9294-3943746bdea33349879676836789606-compressed.jpg.jpeg
Views: 7
Size:  21.3 KB
Are you actually setting x=1 in the expansion of the binomial?
0
reply
RDKGames
Badges: 20
Rep:
?
#10
Report 1 month ago
#10
(Original post by bored_user:))
So is this the answer?
Almost.

Is \displaystyle \sum_{k=0}^n \binom{n}{k} really the series expansion of (1+x)^n ?
0
reply
mqb2766
Badges: 18
Rep:
?
#11
Report 1 month ago
#11
(Original post by mqb2766)
Are you actually setting x=1 in the expansion of the binomial?
(1+x)^n = 1+nx + n(n-1)/2x^2 + ... + x^n
When x=1, the right equals ?
Last edited by mqb2766; 1 month ago
0
reply
bored_user:)
Badges: 22
Rep:
?
#12
Report Thread starter 1 month ago
#12
(Original post by RDKGames)
Almost.

Is \displaystyle \sum_{k=0}^n \binom{n}{k} really the series expansion of (1+x)^n ?
I have no idea what's going on here...

Can you tell me what the correct answer is and explain it please? Thanks
0
reply
RDKGames
Badges: 20
Rep:
?
#13
Report 1 month ago
#13
TBH, you should've come across the binomial theorem (which is also in the Edexcel formula booklet!) when it tells you that

(a+b)^n = \displaystyle \sum_{k=0}^n \binom{n}{k}a^kb^{n-k}

Choosing appropriate values for a,b makes the answer fall out immediately.
0
reply
mqb2766
Badges: 18
Rep:
?
#14
Report 1 month ago
#14
(Original post by bored_user:))
I have no idea what's going on here...

Can you tell me what the correct answer is and explain it please? Thanks
What is the binomial expansion of
(1+x)^n
0
reply
bored_user:)
Badges: 22
Rep:
?
#15
Report Thread starter 1 month ago
#15
(Original post by mqb2766)
(1+x)^n = 1+nx + n(n-1)/2x^2 + ... + x^n
When x=1, the right equals ?
is this it?
Name:  image-446e6ae6-1821-4c49-8b3a-5935681a8e924826274400607781229-compressed.jpg.jpeg
Views: 6
Size:  17.6 KB
0
reply
mqb2766
Badges: 18
Rep:
?
#16
Report 1 month ago
#16
(Original post by bored_user:))
is this it?
Name:  image-446e6ae6-1821-4c49-8b3a-5935681a8e924826274400607781229-compressed.jpg.jpeg
Views: 6
Size:  17.6 KB
Yes. The rows in Pascal triangle sum to 2^n.
0
reply
bored_user:)
Badges: 22
Rep:
?
#17
Report Thread starter 1 month ago
#17
(Original post by mqb2766)
Yes
Omg thank you so much for helping!!!
1
reply
jellybellyb
Badges: 18
Rep:
?
#18
Report 1 month ago
#18
Yep, super tough.

Rufus the red
nikkiblonsky
0
reply
bored_user:)
Badges: 22
Rep:
?
#19
Report Thread starter 1 month ago
#19
(Original post by jellybellyb)
Yep, super tough.

Rufus the red
nikkiblonsky
This is uni stuff lol.
0
reply
Rufus the red
Badges: 17
Rep:
?
#20
Report 1 month ago
#20
(Original post by jellybellyb)
Yep, super tough.

Rufus the red
nikkiblonsky
Sorry about this fool.
1
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Are you travelling in the Uni student travel window (3-9 Dec) to go home for Christmas?

Yes (73)
27.76%
No - I have already returned home (30)
11.41%
No - I plan on travelling outside these dates (54)
20.53%
No - I'm staying at my term time address over Christmas (28)
10.65%
No - I live at home during term anyway (78)
29.66%

Watched Threads

View All